⚛️ general relativity

From massless wormholes to massive black bounces: Relativistic astrophysical observations of shadows and multiple light rings

This paper introduces a framework for generating massive black bounce geometries from massless wormholes, revealing that while these exotic objects can exhibit complex light ring structures and nested shadow features, current Event Horizon Telescope resolution largely washes out these distinguishing characteristics, creating a strong observational degeneracy with standard black holes.

Original authors: G. Alencar, Kirill A. Bronnikov, T. M. Crispim, Diego Sáez-Chillón Gómez, Marcos V. de S. Silva

Published 2026-09-15

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CC BY 4.0

Original authors: G. Alencar, Kirill A. Bronnikov, T. M. Crispim, Diego Sáez-Chillón Gómez, Marcos V. de S. Silva

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the grand theater of the universe, gravity is the director that shapes the stage. For decades, the most famous script has been written by Albert Einstein's theory of general relativity, which describes how massive objects like stars and galaxies bend the fabric of space and time. According to this theory, if enough matter is squeezed into a small enough space, it creates a black hole—a region so dense that nothing, not even light, can escape its pull. At the very center of a traditional black hole lies a singularity, a point where the laws of physics break down and density becomes infinite. This mathematical breakdown has long bothered scientists, suggesting that our current understanding of gravity is incomplete. To fix this, researchers have proposed "regular" black holes, which have a smooth center without a singularity, and "wormholes," which are tunnels connecting two distant points in space. While black holes are observed every day, wormholes remain theoretical, and the line between a black hole with a smooth center and a traversable wormhole has been blurry. Understanding exactly where one ends and the other begins is crucial for interpreting the high-resolution images of the universe's most extreme objects.

A team of researchers has now built a new mathematical bridge between these two cosmic concepts. They started with a theoretical model of a wormhole that has no mass, meaning it does not pull on objects or bend light in the way a heavy star does. By carefully introducing a mass function—a way to add weight to the structure without changing its fundamental shape—they transformed this massless tunnel into a "black bounce." This new family of objects acts as a smooth transition: depending on how much mass is added, the object can behave like a standard black hole with an event horizon, or like a wormhole that allows passage through its center. The researchers applied this method to a specific, well-known wormhole model and created a new, more complex version they call a generalized Bardeen-like black bounce. This new geometry is special because it can possess multiple "light rings"—circular paths where photons (particles of light) can orbit the object—rather than just the single ring found in standard black holes.

The team then simulated how these objects would look to a distant observer, specifically focusing on the "shadow" they cast against the background of glowing gas. They calculated the size of this shadow and compared it to real observations of Sagittarius A*, the supermassive black hole at the center of our own galaxy, captured by the Event Horizon Telescope. Their calculations showed that for a wide range of parameters, the shadow size of these exotic black bounces fits perfectly within the observed data. This means that the strange, smooth-centered objects they modeled are indistinguishable from standard black holes based on the size of their shadows alone. The researchers also mapped out the paths of massive particles and light rays, discovering that the new geometry allows for a much richer variety of orbits. Unlike the simple, single-ring structure of a standard black hole, these objects can trap light in two different unstable orbits separated by a stable one, creating a complex web of potential paths for matter and radiation.

To see what this complexity would look like in a real image, the scientists simulated the view of a thin disk of hot gas swirling around these objects. In their high-resolution simulations, the presence of multiple light rings created a stunning, intricate pattern of nested, bright rings, with distinct gaps and variations in brightness that are far more detailed than the simple ring seen around a standard black hole. The mass of the object and the specific shape of the wormhole throat significantly altered the brightness and spacing of these rings. However, when the researchers applied a filter to simulate the limited resolution of current telescopes, the picture changed dramatically. The fine, nested structures were blurred together, washing out the complex details and leaving behind a single, smooth ring surrounding a dark center.

This blurring effect reveals a significant challenge for astronomers: at the resolution of today's most powerful telescopes, these exotic black bounces look exactly like ordinary black holes. The unique, multi-layered structures that would prove the existence of a wormhole or a smooth center are hidden behind the observational blur. The researchers conclude that while these objects are mathematically valid and fit current data, distinguishing them from standard black holes will require the next generation of telescopes with much higher angular resolution. Until then, the universe keeps its secrets, hiding the intricate dance of light rings behind a veil of observational limits, waiting for sharper eyes to reveal the true nature of the dark centers of galaxies.

Technical Summary: From Massless Wormholes to Massive Black Bounces

Problem Statement
General Relativity (GR) predicts the formation of space-time singularities under gravitational collapse, a theoretical limitation addressed by proposals for regular black holes (e.g., Bardeen) and traversable wormholes (e.g., Ellis-Bronnikov). While "black bounce" geometries have emerged as a class of regular space-times that interpolate between these two extremes by replacing the singular center with a minimal radius (throat), a specific challenge remains: how to introduce a gravitational mass scale into a massless wormhole seed while preserving its intrinsic areal-radius profile. Existing models often alter the geometric structure of the radius function $r(x)$ when introducing mass. This work addresses the need for a framework that generates massive black bounce geometries from massless seeds without modifying the underlying $r(x)$ profile, allowing for a continuous interpolation between traversable wormholes and regular black holes.

Methodology
The authors develop a general framework based on linear deformations of seed geometries.

Framework Construction: Starting with a static, spherically symmetric metric in quasiglobal coordinates ( $ds^2 = -f(x)dt^2 + dx^2/f(x) + r^2(x)d\Omega^2$ ), they introduce a position-dependent mass function $M(x) = m\mu(x)$ . This deformation modifies the temporal metric function $f(x)$ while keeping the areal radius $r(x)$ identical to the massless seed. The Einstein tensor is decomposed into the seed geometry's tensor and a term proportional to the mass $m$ , allowing the massless wormhole to act as a background for the massive deformation.
Application to GEB: The framework is applied to the Generalized Ellis-Bronnikov (GEB) wormhole, characterized by $r(x) = (x^n + a^n)^{1/n}$ (where $n \ge 2$ is an even integer). By choosing a specific mass profile $M(x) = m(x/r(x))^n$ , they derive the Generalized Bardeen-like (GBL) black bounce metric. This metric reduces to the Schwarzschild solution when the throat parameter $a \to 0$ and to the massless GEB wormhole when $m \to 0$ .
Geodesic Analysis: The authors analyze the motion of neutral massive particles and photons. They derive effective potentials, identify circular orbits (stable and unstable), and calculate the Innermost Stable Circular Orbit (ISCO) and photon spheres.
Observational Constraints: The theoretical shadow radius is calculated and compared with Event Horizon Telescope (EHT) observations of Sgr A* to constrain the model's parameter space ( $a$ and $m$ ).
Ray Tracing and Imaging: Using a geometrically and optically thin accretion disk model with a Standard Unbound (SU) emission profile, the authors perform backward ray tracing to simulate optical appearances. They account for gravitational redshift and transfer functions. Finally, they apply a Gaussian beam convolution to simulate the finite angular resolution of the EHT.

Key Contributions and Results

Geometric Interpolation: The GBL metric successfully generates a family of regular space-times that continuously interpolate between massive wormholes and regular black holes. Depending on the parameters, the throat can reside in a static region (wormhole), inside an event horizon (regular black hole with a throat), or coincide with a horizon.
Complex Orbital Structure: Unlike the massless GEB geometry, which possesses only a single unstable circular orbit at the throat, the massive GBL black bounce exhibits a rich orbital structure. The effective potential for massive particles can display multiple critical points, including:
- Two unstable circular orbits (one at the throat, one at a finite radius).
- Stable circular orbits.
- An Innermost Stable Circular Orbit (ISCO) whose radius depends on the parameters $a$ , $m$ , and $n$ .
Multiple Light Rings: The photon sector reveals even more complexity. The GBL geometry can support multiple photon spheres, including configurations with two unstable circular photon orbits separated by a stable one. This leads to a rich light ring structure with multiple critical impact parameters.
Shadow Constraints: When comparing the predicted shadow radius ( $r_s$ $r_{s}$ ) with EHT data for Sgr A*, the model remains consistent with observations.
- For the black hole branch (with horizons), the shadow radius stays within the $1\sigma$ confidence band of EHT measurements.
- For the wormhole branch (horizonless), the throat radius is constrained to $4.55 \lesssim a/m \lesssim 5.22$ ( $1\sigma$ ) and $4.21 \lesssim a/m \lesssim 5.56$ ( $2\sigma$ ).
Optical Appearance and Degeneracy:
- High Resolution: At high resolution, the GBL wormholes with multiple light rings produce distinctive, nested intensity profiles with multiple narrow rings, differing significantly from standard black holes. The presence of stable orbits and multiple unstable orbits creates complex transfer functions.
- Low Resolution (EHT): When the simulated images are convolved with a Gaussian beam representing the EHT's finite resolution, these fine sub-structures (nested rings, sharp transitions) are "washed out." The resulting images appear as a single, smooth emission ring surrounding a central dark region, indistinguishable from standard Schwarzschild or Kerr black holes at current resolution.

Significance and Claims
The paper claims that the proposed framework provides a robust method for constructing massive regular black hole and wormhole geometries that preserve the intrinsic throat structure of massless seeds. The primary significance lies in demonstrating that while these exotic compact objects possess theoretically distinct and rich internal structures (multiple light rings, complex ISCOs), they suffer from a strong observational degeneracy with standard black holes under current EHT resolution.

The authors emphasize that the "fine throat dynamics and light ring structures remain hidden behind the observational blur." Consequently, distinguishing these GBL black bounces from standard GR black holes strictly requires next-generation Very Long Baseline Interferometry (VLBI) or space-based interferometers capable of resolving the high-order photon rings. The paper concludes that while the critical impact parameter alone is insufficient to distinguish these models, the full brightness profile and relative intensity of image components (which are affected by mass deformation and redshift) offer potential avenues for future discrimination, provided resolution limits are overcome.

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